The move is retroactive to May 3.
Padres manager Bud Black said the shoulder remained troublesome and the team decided to give him a full two weeks to rest. Morrow is 2-0 with a 2.73 ERA on the season.
Left-hander Frank Garces, who opened the season with the Padres, was recalled from Triple-A El Paso. He's 0-0 with a 1.59 ERA in six big league appearances.